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June 2016 Shape theorems for Poisson hail on a bivariate ground
François Baccelli, Héctor A. Chang-Lara, Sergey Foss
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Adv. in Appl. Probab. 48(2): 525-543 (June 2016).

Abstract

We consider an extension of the Poisson hail model where the service speed is either 0 or ∞ at each point of the Euclidean space. We use and develop tools pertaining to sub-additive ergodic theory in order to establish shape theorems for the growth of the ice-heap under light tail assumptions on the hailstone characteristics. The asymptotic shape depends on the statistics of the hailstones, the intensity of the underlying Poisson point process, and on the geometrical properties of the zero speed set.

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François Baccelli. Héctor A. Chang-Lara. Sergey Foss. "Shape theorems for Poisson hail on a bivariate ground." Adv. in Appl. Probab. 48 (2) 525 - 543, June 2016.

Information

Published: June 2016
First available in Project Euclid: 9 June 2016

zbMATH: 1342.60010
MathSciNet: MR3511774

Subjects:
Primary: 60D05 , 60F15 , 60G55

Keywords: branching process , heaps , max-plus algebra , Point process theory , Poisson rain , Queueing theory , random closed set , shape , Stochastic geometry , sub-additive ergodic theory , time and space growth

Rights: Copyright © 2016 Applied Probability Trust

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Vol.48 • No. 2 • June 2016
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